On local Poincaré via transportation

By Max-K. von Renesse. 2005

54 citations recorded by the source corpus.

It is shown that curvature-dimension bounds CD(N,K) for a metric measure space (X,d,m) in the sense of Sturm imply a weak L1-Poincaré-inequality provided (X,d) has m-almost surely no branching points.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/483b27bfa87c1442815f5c5d04235cc74aada316

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Geometry and Topology

Citations in the corpus

The globalization theorem for the Curvature-Dimension condition (2016, background): “verifying MCP(K,N) and supp(m) = X also supports a local (1, 1)-weak Poincaré inequality, see [68].”
Local Poincaré inequalities from stable curvature conditions on metric spaces (2011, methodology): “This approach has also been used by other authors, see [18] for a similar proof of the local Poincaré inequality in nonbranching spaces using a related measure contraction property [17, 22].”
Weak curvature conditions and functional inequalities (2005, methodology): “After our research concerning DM was completed, we learned of preprints by Ohta [11], von Renesse [ 12 ] and Sturm [14] that consider somewhat related conditions.”
Finsler interpolation inequalities (2009, methodology): “We refer to [23,24, 33 ] for related work based on the measure contraction property, [28,29] for another approach using the contraction of Markov chains, and to [42, Part III] for further developments.”
Geometry and Analysis of Dirichlet forms (2012, background): “With the additional assumption that (X, d) is non-branching, it was proved in [30, 39] that (X, d, m) supports a weak (1, 2)-Poincaré inequality.”
Geometric Inequalities and Generalized Ricci Bounds in the Heisenberg Group (2009, background): “in [28] for 1 and [32] or [18] with Remark 5.”
Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm (2011, background): “In [14] a local Poincaré inequality was proved in nonbranching metric spaces with nonnegative Ricci curvature, see also [18].”